@aspirant s9 Sorry for the late reply.
Unfortunately I got my straight rejection last week, and I've been waiting since January 6!
I did not apply to VSRP, the adviser had the opportunities posted to our career center website but I went through the same procedure. You basically sit for two interviews, one with the academic adviser you're seeking and the other is with the office of admissions. The adviser gets to assess you academically and discuss your research interest on which he'll base the acceptance/rejection of your application. The second interview is more of casual where the office of admissions ask you about yourself, family, hobbies, how did you know about KAUST, why you chose KAUST, etc (typically 10-15 minutes chat)... If you passed both interviews, the secretary of the center you're going to contacts you for more details to proceed with the visa arrangements. You can check the available VSRP topics on their website, or try contacting a faculty member for a potential position. I'm guessing you start by filling the document on their website, but I skipped this step because the professor already contacted our career center for students.
They have a very strange admission system, I wonder why?!
Hope this helps, best of luck!